Solve 4a^2*2a*a^0

$$4 a ^ { 2 } \cdot 2 a \cdot a ^ { 0 }$$

Evaluate

$$8a^{3}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$4a^{3}\times 2a^{0}$$

To multiply powers of the same base, add their exponents. Add 3 and 0 to get 3.

$$4a^{3}\times 2$$

Multiply 4 and 2 to get 8.

$$8a^{3}$$

Differentiate w.r.t. a

$$24a^{2}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$\frac{\mathrm{d}}{\mathrm{d}a}(4a^{3}\times 2a^{0})$$

To multiply powers of the same base, add their exponents. Add 3 and 0 to get 3.

$$\frac{\mathrm{d}}{\mathrm{d}a}(4a^{3}\times 2)$$

Multiply 4 and 2 to get 8.

$$\frac{\mathrm{d}}{\mathrm{d}a}(8a^{3})$$

The derivative of ax^{n} is nax^{n-1}.

$$3\times 8a^{3-1}$$

Multiply 3 times 8.

$$24a^{3-1}$$

Subtract 1 from 3.

$$24a^{2}$$